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Mr Justice Tugendhat had ruled a tweet she sent – after Newsnight last year wrongly implicated Lord McAlpine in child abuse allegations – was highly defamatory.

Sir Edward Garnier QC told the judge that she had apologised for her “irresponsible use of Twitter”, which caused the peer great distress and embarrassment and agreed to pay him undisclosed damages - which had been given to charity - and his costs.

She had also undertaken never to repeat the allegations about him and had withdrawn them unreservedly.

Mrs Bercow accepted an earlier offer to settle the matter after Mr Justice Tugendhat’s ruling in May that a tweet posed by her was highly defamatory.

Victory: Lord McAlpine (Image: Ian Vogler/ Daily Mirror)

Her posting appeared two days after a Newsnight report last November wrongly implicated the former Conservative Party treasurer in allegations of sex abuse at Bryn Estyn children’s home in the 1970s and 1980s.

Mrs Bercow denied that the tweet was defamatory, but Lord McAlpine, who has already received six-figure payouts from the BBC and ITV, said it pointed “the finger of blame” during a media frenzy.

The judge agreed with Lord McAlpine.

Mrs Bercow’s QC, William McCormick, said today: “Mrs Bercow wishes and hopes that as a result of this matter other Twitter users will behave more responsibly in how they use that platform.